I am thinking about taking a casual tandem ride in the Livermore area. Can anyone recommend a route of about 20-30 miles on scenic roads with very light traffic and not too many hills? A couple of wineries at the beginning/end or along the way would be nice as well.

There's some great routes through Livermore, but beware of the heat this w/e. I'd suggest that you google the "Valley Spokesman Bicycle Touring Club". (valleyspokesmen.org) They have a full list of routes, with details, up and down the Tri-Valley area.